Question 251359: Evaluate the logarithmic equation for three values of x that are greater than -1, three values of x that are between -2 and -1, and at x = -1. Show your work. Use the resulting ordered pairs to plot the graph; submit the graph via the Dropbox. State the equation of the line asymptotic to the graph (if any).
y = log4 (x + 2)
Answer by solver91311(24713)   (Show Source):
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Select any values that you like from the given intervals. Substitute each one, one-by-one, into the given function. Calculate the value of the function, which is to say, the value of  .
This is where you may have a bit of difficulty because I don't know of a handheld calculator that does logs to bases other than 10 and e, and I don't know where you might find a base 4 log table. However, all is not lost. There are several possible solutions.
1. Use the log base conversion formula:
 = \frac{\log_c(x)}{\log_c(b)} = \frac{\ln(x)}{\ln(b)})
2. Use the LOG function in Microsoft Excel. =LOG(number,base) where number is the argument of the log function and base is the value of the base gives you the log to any base you like.
3. Use an on-line logarithm calculator. Several websites offer a log calculator. Submit the base and the argument and you get back the value of the function.
For example: http://www.ajdesigner.com/phplogarithm/log_equation_base_any_y.php
So, do it 7 times, once for each of the specified input values. The points to plot will be the ordered pairs formed by the input value as the first coordinate and the resulting value of the function as the second coordinate.
The asymptote of ) is  , so the asymptote of \right)) must be  such that \ =\ 0) . So just set the function contained in the log argument equal to zero and solve for  . The resulting statement will be the equation of the asymptote.
John
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